Frequency Distribution 44623A

1. **State the problem:** We are given a frequency distribution of high temperatures in classes with their frequencies. We need to complete the table by finding the midpoint, relative frequency, and cumulative frequency for each class. 2. **Formulas and rules:** - Midpoint of a class = $\frac{\text{lower limit} + \text{upper limit}}{2}$ - Relative frequency = $\frac{\text{frequency of class}}{\text{total frequency}}$ - Cumulative frequency = sum of frequencies up to that class 3. **Calculate total frequency:** $$17 + 44 + 68 + 69 + 78 + 68 + 21 = 365$$ 4. **Calculate midpoints:** - $17-27$: $\frac{17 + 27}{2} = 22$ - $28-38$: $\frac{28 + 38}{2} = 33$ - $39-49$: $\frac{39 + 49}{2} = 44$ - $50-60$: $\frac{50 + 60}{2} = 55$ - $61-71$: $\frac{61 + 71}{2} = 66$ - $72-82$: $\frac{72 + 82}{2} = 77$ - $83-93$: $\frac{83 + 93}{2} = 88$ 5. **Calculate relative frequencies:** - $17-27$: $\frac{17}{365} \approx 0.05$ - $28-38$: $\frac{44}{365} \approx 0.12$ - $39-49$: $\frac{68}{365} \approx 0.19$ - $50-60$: $\frac{69}{365} \approx 0.19$ - $61-71$: $\frac{78}{365} \approx 0.21$ - $72-82$: $\frac{68}{365} \approx 0.19$ - $83-93$: $\frac{21}{365} \approx 0.06$ 6. **Calculate cumulative frequencies:** - $17-27$: $17$ - $28-38$: $17 + 44 = 61$ - $39-49$: $61 + 68 = 129$ - $50-60$: $129 + 69 = 198$ - $61-71$: $198 + 78 = 276$ - $72-82$: $276 + 68 = 344$ - $83-93$: $344 + 21 = 365$ 7. **Final table:** | Class | Frequency $f$ | Midpoint | Relative frequency | Cumulative frequency | |--------|---------------|----------|--------------------|----------------------| | 17-27 | 17 | 22 | 0.05 | 17 | | 28-38 | 44 | 33 | 0.12 | 61 | | 39-49 | 68 | 44 | 0.19 | 129 | | 50-60 | 69 | 55 | 0.19 | 198 | | 61-71 | 78 | 66 | 0.21 | 276 | | 72-82 | 68 | 77 | 0.19 | 344 | | 83-93 | 21 | 88 | 0.06 | 365 |